新闻 · arXiv cs.LG

A zero-one law for one-shot system identification

Can a model be identified from one experiment? We study analytic systems that are linearly parameterized by a combination of prescribed dictionary terms, such as partial differential operators and dynamical systems. For a single input-response pair, recovery is possible exactly when the evaluated dictionary terms are linearly independent. We prove a sharp zero-one law: either no input uniquely determines the coefficients, or almost every random input sampled from a nondegenerate Gaussian…